Learn Turkish: Küçücük bir fareyi yakalayabildin mi? - Were you able to catch a tiny mouse?

The root word is küçük (small). When we add the diminutive suffix -cük to emphasize how small it is (meaning 'tiny'), the final k of the root word is dropped. So it becomes küçücük instead of küçükcük. This dropping of the k is a standard rule for words ending in k when they take a diminutive suffix.

Why does fareyi have the accusative ending -i when it says bir (a/an) right before it?

Normally, indefinite objects with bir don't take the accusative ending. However, using bir fareyi (with the buffer -y- and accusative -i) instead of just bir fare shows that the speaker is talking about a specific, particular mouse that was perhaps mentioned before, rather than just any random mouse in general.

Can you break down the suffixes in the verb yakalayabildin?

It starts with the verb root yakala (catch). Then we add the buffer -y-, followed by the ability suffix -abil (to be able to). Finally, we add -di for the past tense and -n for the 'you' (singular) subject. Altogether it builds 'you were able to catch'.

Why is bir placed after küçücük instead of before it?